Recursive procedures are found for calculating the kth-order entropy of non-periodic sequences. These entropies are used as measures of disorder of the sequences and we treat: the Fibonacci sequence and generalizations; the Thue-Morse sequence together with generalizations and the period-doubling sequence. A discussion of the relative ordering of the Thue-Morse and the Fibonacci sequences is given and it is found too simplistic to use any one measure for comparison.